Geometry Questions

Write the coordinates of the vertices after a reflection over the line y 1 10 8 6 TOO U 0 v 4 2 10 8 6 4 2 2 4 618 6 W 8 10 2 4 9 6 ND T 80 U 10

In the diagram below PW 6 and WX 4 Find QX X W P

point Each graph below is the graph of a system of three linear equations in three unknowns of the form Az b Determine whether each system has a solution and if it does the number of free variables A choose D choose 8 choose choose choose F choose

In the figure below mJKM 92 KL bisects JKM and KN bisects LKM Find mZMKM m2NKM

Extra Practice In Exercises 1 4 classify the polygon by the number of sides Tell whether it is convex or concave 3 TODO 1 2 4 In Exercises 5 8 find the perimeter and area of the polygon with the given vertices 5 X 2 4 Y 0 2 Z 2 2 6 P 1 3 Q 1 1 R 4 2 7 J 4 1 K 4 2 L 6 2 M 6 1 8 D 5 3 E 5 6 F 2 6 G 2 3

1 4 Notetaking with Vocabulary continued In Exercises 9 14 use the diagram 9 Find the perimeter of AABD 10 Find the perimeter of ABCD 11 Find the perimeter of quadrilateral ABCD 12 Find the area of AABD 13 Find the area of ABCD 14 Find the area of quadrilateral ABCD D 4 1 C 1 5 Ay 2 A 2 4 4 x B 2 1

18 Do you remember the daisy construction from Chapter 0 Construct a circle with radius s With the same compass setting divide the circle into six congruent arcs Construct the chords to form a regular hexagon inscribed in the circle Construct radii to each of the six vertices What type of triangle is formed What is the ratio of the perimeter of the hexagon to the diameter of the circle

11 In the figure at right what is mPQ mPRQ La bas To Tadil TOW sigasi Poel sit com c 12 Use your compass and protractor to make an arc with measure 65 Now make an arcuri 110 with measure 215 Label each arc with its measure O 13 Name two places or objects where concentric circles appear Bring an example of a set of concentric circles to class tomorrow You might look in a magazine for a photo or make a copy of a photo from a book but not this book 14 Sketch two circles that appear to be concentric Then use your compass to construct a pair of concentric circles R e

9 Sketch the path made by the midpoint of a radius of a circle if the radius is rotated about the center

20 Earth takes 365 25 days to travel one full revolution around the Sun By approximately how many degrees does the Earth travel each day in its orbit around the Sun 21 Earth completes one full rotation each day making the Sun appear to rise and set If the Sun passes directly overhead by how many degrees does its position in the sky change every hour

25 A 38 40 a 9 72 m b 11 8 m

24 C 68 5 c 258 cm b 386 cr

13 A 29 7 b 41 5 ft a 27 2 ft

23 B 72 2 b 78 3 m c 145 m

J B 74 3 a 859 m b 783 m

Respond to each of the following a Explain why Figure A is not the image of Figure B after a rotation about point P B B P A b Explain why Figure B is not the image of Figure A after a reflection across line l A

left 2 Select all the sequences of transformations that could map Figure X onto N Y O X A a single translation B a single reflection C a single rotation D a reflection then a different reflection E a translation then a reflection X

Use the given E 1 F H Statement G J K Given EF JK FG HJ Prove EG HK Reason Send To Proof Send To Proof Send To Proof

3 For which pair of figures can Figure Y a Pair 1 b Pair 2 A c Pair 3 Z A Pair 1 B B Z joue beenwoh etinu ewol s syslane T O 4 Refer to the three pairs of figures shown For each pair of figures determine which single transformation translation rotation or reflection maps Figure A onto Figure B C M Z Pair 2 B sagrit to main Shoillaog A hupit s toolog A iubit alsio 8 ods Balvolbolo Pair 3 00 A B

5 Draw the image of the quadrilateral shown after a 180 clockwise rotation about point al pupil vow nislax P

graph of the function y 2 was transformed according to the transformations given below resulting in the graph of the function y a z b c for some constants a b and c 1 reflection over the x axis 2 vertical shrink 3 horizontal shift left 4 vertical shift up Eleanor was asked to provide a possible value for a b and c She said a Determine if each of her values are reasonable and give reasons for your answers 10 Using the graph of g x shown sketch the transformation g x 2 on the same coordinate grid 4 4 43 1 5 3 O M b 4 and c 7 2 3 4 10

Which of the following is true 1 2 B C 70 A m BCD mzDBC 10 B m BCD m DBC 20 C m BCD m DBC 60 D m BCD m DBC 80 130 D

Write an inequality in slope intercept form from the linear inequality graphed below y 10 10 8 64 2 8 6 4 2 24 008 8 4 6810

144 5 4 56 3 2 m 1 m42 m43 m24 m25

The owner of a convenience store installs two security cameras represented by points C1 and C2 Both cameras point towards the centre of the store s cash register represented by the point R The following diagram shows this information on a cross section of the store 2 8 1 0 6 4 diagram not to scale C2 3 1 The cameras are positioned at a height of 3 1 m and the horizontal distance between the cameras is 6 4 m The cash register is sitting on a counter so that its centre R is 1 0 m above the floor The distance from Camera 1 to the centre of the cash register is 2 8 m Determine the angle of depression from Camera 1 to the centre of the cash register Gi

The diagram below shows a helicopter hovering at point H 380 m vertically above a lake Point A is the point on the surface of the lake directly below the helicopter helicopter 380 H 40 B 25 diagram not to scale Minta Minta is swimming at a constant speed in the direction of point A Minta observes the helicopter from point C as she looks upward at an angle of 25 After 15 minutes Minta is at point B and she observes the same helicopter at an angle of 40 a Write down the size of the angle of depression from H to C

the IB SL formula booklet Round to 3 s f if not otherwise specified 21 A garden includes a small lawn The lawn is enclosed by an arc AB of a circle with centre O and radius 6 m such that AOB 135 The straight border of the lawn is defined by chord AB The lawn is shown as the shaded region in the following diagram diagram not to scale 135 ing cal B a A footpath is to be laid around the curved side of the lawn Find the length of the

For Exercises 2 9 use the diagram at right Points E P and is the center of the circle 2 Name three chords 3 Name one diameter 4 Name five radii 5 Name five minor arcs 6 Name two semicircles 7 Name two major arcs 8 Name two tangents 9 Name a point of tangency 10 Name two types of vehicles that use wheels two household appliances that use wheels and two uses of the wheel in the world of entertainment H A E B P F C G

1 In the photos below identify the physical models that represent a circle a radius a chord a tangent and an arc of a circle ction tools for Exercises 12 17 18 22 23

11 Triangle EFD was made by reflecting triangle ABC across 12 B 2 24 71 6 2 83 63 4 45 3 00 A B C Name pairs of corresponding angles from triangles ABC and EFD rocponding sides from triangles ABC and EFD then translating E D 3 00 63 4 45 2 24 71 6 2 83 F

K P K M N N 4 Here is quadrilateral KLMN after a rotation around M KLMN and its image degree counterclockwise

17 BLUE FISH F H 6 E 6 B U L 6 18 RECTANGL G R T C 12 did in 19 Imagine using two congruent triangles to create a special quadrilateral as you the investigation a What type of triangles do you need to form a rectangle Explain b What type of triangles do you need to form a square Explain

A birthday party caterer counted the number of juice cups on the table The cups contained different flavored juices and different shaped straws Orange juice Grape juice Heart shaped straw Star shaped straw 2 3 4 6 What is the probability that a randomly selected cup contains a star shaped straw given that the cup contains orange juice Simplify any fractions

B 6 A 3 A X E 4 D Yukar daki ekilde m BAD g re AE x ka cm dir C B 4 C 5 ABC bir ikizkenar gen AB AC AD BC ED 4 cm BD 6 cm m DCE oldu una D 6 E 8 00

If U I Y point I is between points U and Y and IY 3 1 and UY 91 find UI

What does the notation Rx axis DAB mean Reflection Rotation Clockwise Counter clockwise Around the origin to the axis Over the x axis Over the y axis 180 90 270

In the figure below C is between A and D and B is the midpoint of AC If BC 4 and AD 11 find CD CD 1 D X 5

6 What if a restaurant needed to build a wheelchair ramp for its customers The angle of elevation for a ramp is recommended to be 5 degrees If the vertical distance from the sidewalk to the front door is 2 feet what is the horizontal distance that the ramp will take up x How long will the ramp be z Round your answers to the nearest hundredth 3 points z 2 09ft x 61ft

8 To estimate the weight of pumpkins for the pumpkin farm a farmer took a random sample of 30 pumpkins The weights to the nearest tenth of a pound of those 30 randomly sampled pumpkins is given by the table below Answer each question 12 pts 2 5 17 0 7 3 4 0 7 9 8 0 11 9 12 0 15 9 16 0 19 9 9 1 13 4 14 4 A Construct a histogram for the number of victories Use the following classes Label your graph as needed 3 pts 0 3 9 16 7 3 1 5 1 9 3 6 0 2 4 6 0 10 3 19 Shape Center Spread B Identify the five number summary to the nearest undredth 1 pt 1 9 5 6 12 0 D Create a boxplot for the number of victories You can place your boxplot anywhere on the vertical portion of the graph 3 pts 10 8 6 4 2 0 9 5 y 505 6 8 8 4 0 Frequency 4 10 3 12 8 9 9 4 8 18 3 7 6 8 Pumpkin Weight lbs C Identify the mean and standard deviation to the nearest hundredth 1 pt 4 8 12 16 Pumpkin Weight lbs E Describe the shape center spread and unusual features for the weights of the pumpkins 4 pts 5 6 2 6 15 1 12 16 20 X ix 20

What is an angle An angle is I

1 point What is a radian a radius that is 3 14 inches long an angle measure with an arc length equal to one diameter length an arc length that is the length of one diameter an angle measure with an arc length equal to one radius length Previous

1 point A hula hoop has a radius of 19 inches What is the length of the arc subtending 1 4 of the hoop 59 7 inches 29 8 inches 14 9 inches 43 8 inches

B 1 point A circle has a circumference of 28 centimeters If an arc subtends a central angle of 55 degrees what is the arc length 8 56 centimeters 26 88 centimeters 53 76 centimeters 4 28 centimeters

5 1 point Area of sector is to O circumference of circle circle area diameter semicircle as arc measure is to 360 degrees

9 1 point A pizza has a radius of 7 inches If it is cut into 6 equal slices what is the area of each slice 7 33 square inches 14 66 square inches 49 square inches 25 66 square inches Previous

1 1 point A plane slices through a cone parallel to the base What shape is the cross section oval triangle square circle 0000

7 1 point How many radians are in a semicircle 00 T EN EN 3 01 2 2

3 1 point A sector of a circle has a central angle measure of 310 degrees If the radius of the circle is 2 feet what is the area of the sector 12 31 square feet 10 82 square feet 5 41 square feet 21 64 square feet 000

to the coordinate grid 5 4 Find point Q on RS that is of the distance from R to S 8 3 5 Find point D on AB that is of the distance from A to B 6 Find point G on AB such that the ratio of AG to GB is 3 2 A R Ay O U M M B S M

d y 46 O C 4 d y 4 b 2 y 4 2 T b do not shift up or down do not shift left or right shrink vertically neither stretch nor shrink horizontally a shrink vertically neither stretch nor shrink horizontally do not shift up or down Shift lefUright a 4 d 4 c by a factor of by a factor of 6 by a factor of by a factor of X 6 by a factor of by a factor of units units 4 units units O 4 units C C a y How is the graph in part b related to the graph in part a If a graph is not supposed to be stretched or shrunk enter 1 in the corresponding box on the right If a graph is not supposed to be shifted in some direction enter 0 in the corresponding box on the righ Do not reflect a 12 b b d 4 How is the graph in part c related to the graph in part a If a graph is not supposed to be stretched or shrunk enter 1 in the corresponding box on the right If a graph is not supposed to be shifted in some direction enter 0 in the corresponding box on the right Reflect across the x axis d 6 X X How is the graph in part d related to the graph in part a If a graph is not supposed to be stretched or shrunk enter 1 in the corresponding box on the right If a graph is not supposed to be shifted in some direction enter 0 in the corresponding box on the right Reflect across the x axis shrink vertically neither stretch nor shrink horizontally do not shift up or down